I would disagree as well. Most Slavic languages are much less closely related than Roman languages for example. I'm a native Bulgarian speaker and while I can catch some words when travelling in Serbia it's not that straightforward to understand others or to explain myself. I can understand people better in Croatia actually, which is kinda weird cause we don't share a common border. If I go to Poland, the gap becomes even wider. But for both the gap is significant. Grammar is different (e.g. inflections vs no inflections), pronunciation is different, hell even the alphabets are different.
